1. Field of the Invention
The present invention relates to a technique for generating threshold matrixes which are compared with a multicolor original image in generating halftone images representing the original image, and also relates to a technique for generating the halftone images representing the multicolor original image.
2. Description of the Background Art
To print an original image of gray scale (i.e., continuous tone), halftone dots are used in many cases. In a generally-used AM (Amplitude Modulated) screening, grayscale representation is made by changing the size of dots which are regularly arranged two-dimensionally at predetermined angles and pitch (accurately, the dots are clusters each of which is a group of dots (or pixels) connecting one another). Halftone images of a plurality of color components where arrangement directions of halftone dots are tilted one another are generated in printing a color original image. For example, in generating halftone images of yellow, cyan, magenta, and black, arrangement directions of halftone dots in the halftone images of respective colors, are tilted relatively to arrangement directions (hereinafter, referred to as “reference arrangement directions”) of pixels of the original image by 0, 15, 45, 75 degrees, and thereby, moire appearing by overlaying a plurality of halftone images (especially, second-order moire appearing by overlaying halftone dots of cyan, magenta, and black) is made less obvious.
In generation of a halftone image, generally used is a technique where a threshold matrix in which a plurality of elements are arranged in a row direction and a column direction and a threshold value is assigned to each of the elements is prepared and an original image is compared with the threshold matrix. In this case, since an angle Ψ of arrangement directions of halftone dots relative to the reference arrangement directions is represented by the arctangent of (n/m) (n and m are positive integers equal to 1 or more) (i.e., (tan Ψ=n/m)), the technique using the threshold matrix is also called as a rational tangent method. In the rational tangent method, it is impossible to set arrangement directions of halftone dots relative to the reference arrangement directions to 15 degrees accurately, and an approximate value is used by changing the angle Ψ to the arctangent of (1/3), (3/11), (5/19), (7/26), or the like (similarly in 75 degrees). In a case where a halftone image where the angle Ψ of arrangement directions of halftone dots relative to the reference arrangement directions becomes the arctangent of (n/m) is generated with the threshold matrix, it is known that (m2+n2) halftone dots are included in an area in the halftone image corresponding to one threshold matrix (i.e., the minimum size of threshold matrix which is settable) (the relationship between the rational tangent (tan Ψ=n/m) and the number of halftone dots is described in, for example, Japanese Patent Application Laid-Open No. 57-171337 (Document 1), page 3, lines 11 to 15 in the upper right column).
If a halftone image of the third color component where halftone dots are arranged in directions tilted relatively to the reference arrangement directions by 45 degrees is overlaid on halftone images of the first and second color components where angles of arrangement directions relative to the reference arrangement directions are approximate values of 15 and 75 degrees, the pitch of halftone dots of the first and second color components being the same as that of the third color component, there is a case where second-order moire easily appears actually (i.e., second-order moire with a long cycle appears). Japanese Patent Application Laid-Open No. 52-139501 (Document 2) discloses a technique for, in the combination of such halftone images, obtaining a pitch of halftone dots in the halftone image of the third color component (the halftone dots arranged in arrangement directions tilted by 45 degrees relatively to the reference arrangement directions) as a value which is capable of suppressing appearance of the second-order moire, by performing a computation using the pitch of halftone dots and angles of the arrangement directions in the halftone images of the first and second color components.
In an apparatus for recording an image on a recording surface where a plurality of irradiation positions of light beams arranged in a predetermined width direction are moved in a main scan direction perpendicular to the width direction, if there is a light beam whose intensity is larger than the other light beams in a case where an angle formed between one of arrangement directions of halftone dots in a halftone image and the main scan direction is set to 0 or 45 degrees, the halftone dots are arranged in the main scan direction (also in a case where the arrangement directions are tilted relatively to the main scan direction by 45 degrees, the halftone dots seem to be arranged in the main scan direction) and large dots (elements of halftone dots) are written at the same positions in the width direction by influence of the light beam, to thereby cause banding unevenness (streak unevenness). Japanese Patent Application Laid-Open No. 6-130656 (Document 3) discloses a technique for setting each of angles formed between arrangement directions of halftone dots and a main scan direction to other than 0 and 45 degrees in halftone images of three color components with suppression of appearance of the second-order moire. Document 3 also discloses a technique for obtaining arrangement directions of moire elements appearing in overlaying two halftone images and a pitch of the moire elements.
Well known is a technique where a threshold arrangement corresponding to one halftone dot where threshold values are arranged two-dimensionally, is prepared, coordinate values in a coordinate system of the threshold arrangement which correspond to respective pixels in an original image, are obtained with predetermined angles and pitch so that halftone dots are arranged at the angles and the pitch in the halftone image, and values of the pixels are compared with threshold values in the coordinate values to generate the halftone image (for example, see Japanese Patent Application Laid-Open No. 60-165873). In this technique, since the angles of arrangement directions of halftone dots are treated as irrational tangents, the technique is also called as an “irrational tangent method”.
In the meantime, in overlaying halftone images of three color components, appearance of the second-order moire can be suppressed by using the techniques of Documents 2 and 3, however, in this case, pitches and arrangement directions of halftone dots in halftone images are limited greatly. Therefore, required is a new technique which is capable of determining the pitches and the arrangement directions of halftone dots in the halftone images widely with suppressing the second-order moire.